Stochastic evolution, or Ito-Langevin, equations provide mathematical descriptions of the spatial motion, local interaction, and stochastic fluctuation effects of randomly distributed populations. They frequently serve as models for measure-valued stochastic processes, also called random measures, arising in the studies of such fields as epidemiology, ecology, population genetics, chemical kinetics, economics, and neutron and radiative transport. Our proposed research concerns several such processes. One arises as the continuous state-space version of the Ohta-Kimura ladder model for the distribution of electrophoretically detectable alleles in a genetic population. Another, called the stochastic measure diffusion process, is the continuous analogue of an infinite-particle branching Markov system and arises in models of disease control and epidemiology, as well as in other areas. We intend to continue our present lines of research on these processes, with the objective of providing descriptions of the distribution and concentration of such populations in both the long and short term. The techniques to be employed will be primarily mathematical, drawing from the fields of probability, statistics, and applied analysis.